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Here I have a mind to shew how several questions, usually solved by the Rule called Position, may more easily and intelligibly be solved. In order thereto it is only necessary to consider the contrast, already taken notice of between Addition and Subtraction; between Multiplication and Division, viz. that whatever is effected by the one is unravelled by the other.

One being asked how old he was answered, if my age be doubled, the # and ; of my age added to it, more 1 year, I should be 100 years old. What is his age?

Answ. 36 years.

Here from the last number 100 given I easily discover the number sought: for being doubled, i. e. multiplied by 2; the # and ; added, that is multiplied likewise by ; and #, the sum of the products more 1, makes 100; consequently the sum of the products is 100 less 1. viz. 99. Then since the numbe, sought multiplied by 2, by ; by 4. respectively, the sum of the products is 99; if it be multiplied by *, the sum of these multipliers, the product will

be likewise 99. Therefore we have given the product 99 and the multiplier 23 to find the multiplicand. From 100 Take I w 2}=11 99 2} 99 4. 4. l 4. 1 1 I I 11) 396 4. 396 36 11) 396 36 CHAP. VII.

THE RULE OF THIREE IN FRACTIONS. A

NHE Rule of Three in Fractions, is analogous to the Rule of Three in whole Numbers, both in the Stating and Operation, For - Thi e

- s

The first and third number or fraction must be of the same name or kind, and reduced to fractions of the same name or denominator.

Multiply the second and third terms together and divide the product by the first; the quotient is the fourth term required; due regard being had to the rules laid down for multiplying, dividing and reducing fractions.

Note. When the first term is 1, the fourth is found by multiplying the second and third; and when the second or third is I, the fourth is found by dividing the other by

the first. w

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3 14. Divide by-> — the product of ; into 3. - 4. 24

2. If ; of a yard cost #:l, what will 3 yard cost? Austw. 10s. 3. What will #5. cost, if #s buy #ib. ? Answ. 4%; d. 4. If 19:h cost#l, what quantitity can I have for is..? Answ. 3 #5. 5. What wil; Cwt, come to is 63. Cwt, cost 21 #1.” Answ. 11. 12s. 23d, 6. How many ib of pot-ashes can I have for 12; if lib cost #d. Answ. 71b. 7. If for 10ts. I buy one hundred of oranges; how many hundred can I have then for 105}s.? Answ. 10; hundred. 8. If Ith of anything cost 5;s what will come to? Answ. 48.7%d. - 9, How much will: Cwt, come to, at the rate of 153s. the Cwt. Answ. 3s. 11; d. Although the method before laid down be universally applicable, as by the foregoing examples appeareth, yet there are other methods more ready and accommodate in practice in some particular cases. - JRule

Rule I.

If the first and third terms be fractions, and the second

t, reduce the said first and third to one common deno

inator; then rejecting the denominators, I make the mumerator of the first, the first term, and the dumerator of the third, the third term, and work as in whole numbe

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If of the first and third terms one be 1, and the other a fraction, put the denominator of the fraction instead of 1, and the numerator in the place of the fraction, and work the question as in whole numbers as before.

Application.
14. If I ton of tallow cost 357. what cost 3 of a ton
4—35 3

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Rule III.

Gf the first and third, if one be a whole number and the other a fraction, multiply the whole number by the denominator of the fraction and work as before. Or if one be a whole number and the other a mixed number, bring the mixed number to an improper fraction and put the numerator-in the place of the fraction or mixed number, and multiply the whole number by the denominator of the fraction and place the product in the room of the said whole number,

- Application. 20. If a piece of cambric 15 yards long cost 31, 15s.

what cost ; yard

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Rule IV.

If the second term be a fraction likewise, the first and third being brought to one denomination, multiply the first by the denominator of the second for a divisor, and the third by the numerator of the second for a dividend, divide the last by the first and the quotient is the answer.

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